Computers Articles

Cheat Sheet / Updated 10-31-2023

So, you’re using a Mac running macOS Sonoma? Good job! This Cheat Sheet warns you about six moves to avoid at all costs, gives you a handy reference of keyboard shortcuts that can save you time, teaches you how to navigate the "Save As" dialog using the Tab key, explains a straightforward protocol for backups, and tells you how to burn CDs from the Music app.

Article / Updated 10-31-2023

Imagine flipping a coin in the air. As it’s spinning, is it showing heads or tails? Well, you can't know the answer while the coin is spinning. Only when the coin lands and settles down does it display a definite result. When asking the question "how does quantum computing work?" think of that uncertainty you see while the coin is spinning — it's like the uncertainty we capture and use in quantum computing. We put many processing elements — qubits — into a state of uncertainty. Then we program the qubits, run the program, and capture the results — just like when the coin lands. Don't have time to read the entire article? Jump to the quick read summary. How does a quantum computer work? Quantum computing is different from the fixed 0s and 1s, bits and bytes, used in today’s devices. Quantum computing is based on quantum mechanics, a branch of physics that can be hard to comprehend. But the way in which quantum computing deals effectively with large degrees of uncertainty feels like the way we make many of the decisions we encounter in daily life. Quantum computing is complementary to classical computing, the kind of computing we use today, not a replacement for it. By working with uncertainty, we can take on some of the biggest, most complex problems that humanity faces, in a new and powerful way. Quantum computing will solve problems for which today’s computing falls short — problems in areas such as modeling the climate, drug discovery, financial optimization, and whether or not it’s a good morning to launch a rocket. And this technology is just getting started. Many advanced quantum computers run only for a fraction of a second at a time. However, steady progress is being made. Even now, at this early stage, quantum computing is inspiring us to, as a sage once said, “think different” about the way we use existing computing capabilities. Those betting on the success of these machines see many potential quantum computing applications, including in the fields of medical science and health care, cryptology, climate change abatement, insurance risk assessment, finance, and more. Understanding why quantum computing is so strange Quantum computers have a sense of strangeness about them, almost a mystical aura. (The 2022 movie, Dr. Strange in the Multiverse of Madness, captures some of the feeling that people have about quantum mechanics in general.) Why is this? There are two main reasons. The first reason is people’s fundamental misunderstanding of the nature of matter, which quantum mechanics explains. The second is the incredible power that quantum computing, when mature, is expected to deliver to humanity. How does quantum mechanics change people’s view of the world? The world we live in, where rocks fall down and rockets go up, seems to be dominated by solid matter, with energy as a force that acts on matter at various times. Yet matter can simply be seen as congealed energy. Most of the mass of the protons and neutrons inside the nucleus of an atom, for instance, is simply a bookkeeper’s description of the tremendously powerful energetic fields that keep these particles in place. One of the most important kinds of particles in quantum computing, photons, have no mass at all; they are made up of pure energy. And it was Einstein himself who told us that matter and energy are equivalent, with his famous equation, E=mc2. To translate: The energy contained in solid matter equals its mass times the speed of light squared. The speed of light is a very large number — 300,000 km/second, or 186,000 miles/second. Squaring the speed of light yields a far larger number. Plug this very large number into Einstein’s famous equation and you'll see that there is a lot of energy in even small amounts of matter, as demonstrated by nuclear power plants and nuclear weapons. The point is that, in quantum mechanics, matter is relatively unimportant; particles act more as bundles of energy. And quantum computing takes advantage of the exotic properties of these particles — ionized atoms, photons, superconducting metals, and other matter that demonstrates quantum mechanical behavior. The second reason that quantum computers get such a strong emotional reaction is the tremendous power of quantum computing. The best of today’s early-stage quantum computers are not much more powerful, if at all, than a mainstream supercomputer. But future quantum computers are expected to deliver tremendous speedups. Over the next decade or two, we expect quantum computers to become hundreds, thousands, even millions of times faster than today’s computers for the problems at which they excel. People can’t really predict, nor even imagine, what it’s going to be like to have that kind of computing power available for some of the most important challenges facing humanity. That future is very exciting, yes. But it’s also a bit, as Einstein described quantum mechanics, “spooky.” Grasping the power of quantum computing To help you get started in understanding quantum computing, here are five big ideas to get your head around: Qubits: Qubits are the quantum computing version of bits — the 0s and 1s at the core of classical computing. They have quantum mechanical properties. Qubits are where all the magic happens in quantum computing. Superposition: While bits are limited to 0 or 1, a qubit can hold an undefined value that is neither 0 nor 1 until the qubit is measured. The capability to hold multiple values at once is called superposition. Entanglement: In classical computing, bits are carefully separated from each other so that the value of one does not affect others. But qubits can be entangled with each other. When changes to one particle cause instantaneous changes to another, and when measuring a value for one particle tells you the corresponding value for another, the particles are entangled. Tunneling: A quantum mechanical particle can instantaneously move from one place to another, even if there’s a barrier in between. (Quantum computing uses this capability to bypass barriers to the best possible solution.) This behavior is referred to as tunneling. Coherence: A quantum particle, such as an electron, that is free of outside disturbance is coherent. Only coherent particles can exhibit superposition and entanglement. How are these terms related? Here’s an example: A good qubit is relatively easy to place into a state of coherence and maintain in a state of coherence, so it can exhibit superposition and entanglement, and therefore can tunnel. (The search for “good qubits” is the subject of a lot of work and controversy today.) These five terms are at the heart of the promise of quantum computing and are involved in many of the challenges that make quantum computing difficult to fully implement. In this section, we describe each of these crucial concepts. Classical computing describes the computers we use every day, which includes not only laptop and desktop computers but also smartphones, web servers, supercomputers, and many other kinds of devices. The term classical computing is used because classical computers use classical mechanics, the cause-and-effect rules of the road that we see and use in our daily lives, for information processing. Quantum computing uses quantum mechanics — which is very different, very interesting, and very powerful indeed — for information processing. Introducing Puff, the magic... qubit? Bits power classical computing — the laptops, servers, smartphones, and supercomputers that we use today. Bit is short for binary digit, where digit specifies a single numeral and binary means the numeral can have only one of two values: 0 or 1 — just like the results of a coin flip. In a computer, bits are stored in tiny, cheap electromechanical devices that reliably take in, hold, and return either a 0 or a 1 — at least until the power is turned off. Because a single bit doesn’t tell you much, bits are packaged into eight-bit bytes, with a single byte able to hold 256 values. (28 — all possible combinations of 8 binary digits — equals 256.) A qubit is a complex device that has, at its core, matter in a quantum mechanical state (such as a photon, an atom, or a tiny piece of superconducting metal). The qubit includes a container of some kind, such as a strong magnetic field, that keeps the matter from interacting with its environment. A qubit is much more complex and much more powerful than a bit. But qubits today are not very reliable, for two reasons: They’re subject to errors introduced by noise in the environment around them. A result of 0 can be accidentally flipped to a result of 1, or vice versa, and there’s no easy way to know that an error has occurred. It’s hard to keep qubits coherent, that is, capable of superposition, entanglement, and tunneling. The situation with qubits today is somewhat like the old joke about a bad restaurant: “The food is terrible — and the portions are so small!” With qubits, the error rates are high and the coherence period is short. But despite these problems, quantum computers do deliver valuable and interesting results while up and running. In quantum computers, qubits are much more complex and far more expensive than bits. Nor are they as easy to manage — but they are far more powerful. The photo below shows a quantum computing module from IBM, suspended at the bottom of a cooling infrastructure that keeps the superconducting qubits at a temperature near absolute zero. Until it's measured, each qubit can represent an infinite range of values between 0 and 1. How does the qubit hold all these values? At the core of the qubit is a quantum particle — a tiny piece of reality in the form of a photon, an electron, an ionized atom, or an artificial atom formed using a superconducting metal. IBM is not the only technology company developing this new technology. Here are some other quantum computing companies: Google, D-wave, Microsoft, Amazon, Intel, Alibaba Group, Atos Quantum, Toshiba, and Rigetti. For quantum computing, the quantum particle at the core of the qubit must be kept in a coherent state — uncontrolled, like the flipped coin while it’s spinning in the air. In a coherent state, we don’t know whether the value of the qubit at a given moment is 0 or 1. When we measure the state of the qubit, the calculation we want to make is performed, and the qubit returns 0 or 1 as a result. Much of the power of qubits comes from the fact that they behave in a probabilistic manner; a given qubit, running the same calculation multiple times without errors, may produce a 0 on some runs and a 1 on another. The final result consists of the number of times each qubit returns a 0 or a 1. So the result of most quantum calculations is a set of probabilities rather than a single number. Qubits are hard to create and hard to maintain in a state of coherence; they also tend to interfere with nearby qubits in an uncontrolled fashion. Taming qubits is one of the biggest challenges to overcome in creating useful quantum computers. A popular approach to building quantum computers involves the use of superconducting qubits, which must be kept at a temperature very close to absolute zero to minimize interference due to heat and, in many cases, to maintain superconductivity. Classical computers are designed to work at room temperature, but they tend to generate heat and to stop working properly as the temperature rises. The need to dissipate heat prevents device makers from packing components as tightly as they would like without resorting to expensive and clumsy solutions such as water-cooling or refrigerating the components. In quantum computing, each additional qubit adds exponentially to the power of the computer. But because qubits tend to interfere with each other, adding more is difficult. IBM, a leader in quantum computing, has published a roadmap showing past and future increases in the number of qubits that power its current and upcoming quantum computers. If you're interested in staying up to date on the development of this technology, here are some places to find quantum computing news: Phys.org; The Quantum Insider; MIT News; Quantum Zeitgeist. Quick Read Summary Quantum computing is a revolutionary field that taps into the strange and mysterious world of quantum mechanics. To grasp its essence, consider the uncertainty of a spinning coin before it lands; this uncertainty mirrors the core principle of quantum computing. In quantum computing, we utilize qubits, which, like the spinning coin, exist in a state of uncertainty until measured. Unlike classical computing, where information is processed as fixed 0s and 1s, quantum computing leverages quantum mechanical properties to process data in new ways. It complements classical computing rather than replacing it, offering a potent tool to tackle complex problems involving substantial uncertainty, such as climate modeling, drug discovery, and financial optimization. Although quantum computing is in its early stages, it shows promise in diverse fields, including medical science, cryptology, climate change mitigation, finance, and more. Its aura of strangeness and potential stems from two key factors: a profound shift in understanding matter and its tremendous computational power. Quantum mechanics reveals that matter is essentially congealed energy, with particles behaving more like bundles of energy than solid entities. Einstein's E=mc² equation underscores this equivalence between matter and energy, highlighting the immense energy stored even in small amounts of matter. Quantum computing harnesses the unique properties of quantum particles like photons, electrons, and ionized atoms to perform computations. Qubits, the quantum counterparts of classical bits, are central to this technology. Qubits can exist in a state of superposition, holding undefined values of 0 and 1 simultaneously until measured. They can also become entangled, enabling instantaneous changes in one qubit to affect another. Additionally, quantum particles can tunnel through barriers, a phenomenon exploited in quantum computing to find optimal solutions. Coherence, the state of being free from outside disturbance, enables particles to exhibit superposition and entanglement. While quantum computers today are not significantly more powerful than classical supercomputers, future quantum machines are expected to offer unprecedented speedups, potentially becoming millions of times faster. This quantum leap in computing power presents exciting but also "spooky" prospects. In summary, quantum computing is poised to transform problem-solving by embracing the uncertainty of quantum mechanics. Key concepts include qubits, superposition, entanglement, tunneling, and coherence, all contributing to the promise and challenges of this cutting-edge technology. Companies like IBM, Google, and Microsoft are at the forefront of quantum computing research, while applications span various domains, from healthcare to finance. Quantum computing's potential is as enigmatic as the spinning coin, but its impact promises to be profound. Hungry for more? Go back and read the article or check out the book.

Article / Updated 09-19-2023

The entire advantage of quantum computing is that it will execute certain specific computer algorithms much, much faster than the classical computers we use today. There's still a long way to go in making these very complex computers work, but even without diving into the details, we can describe the types of things that quantum computing will be very, very good at. And we can give a general idea as to which of these improvements might be available sooner rather than later. Thinking in triplicate There are three broad categories of quantum computing applications. It’s useful to examine each task you’re trying to accomplish from all three of these viewpoints. Applying quantum computing to real-world problems is a creative task, especially in these early days, and using multiple viewpoints can only be helpful. Here are the three approaches: Simulation: In simulation, qubits — trapped bits of coherent matter — mimic other coherent matter, such as the individual atoms within a molecule that might become a medically useful drug. Simulation is arguably the most natural fit for quantum computing because quantum mechanics is what governs the laws of, well, nature. Optimization: A group of qubits can be used as a kind of computational furnace that can be guided into yielding a very good — but not necessarily perfect — solution to a problem. The result might be the right answer, or it may instead be something close to that. (A very good solution to a route-planning or investing problem might save, or make, you a lot of money, even if it isn’t the best possible answer.) Calculation: This approach is, conceptually, the most like the classical computing problem-solving we’re all used to. In calculation, qubits are combined into logic gates, making up a universal computer. When used as logic gates, qubits can solve any imaginable problem, and a quantum universal computer can solve some important problems far faster than today’s computers — which also fit the “universal computer” description — but grind to a near-halt for some problems. We can view the three categories of quantum computing applications as different types of math problems. Simulation requires solving differential equations; optimization requires combinatorial, well, optimization; and calculation requires solving complex problems in linear algebra and involves a lot of matrix math. Both the features used in machine learning and the operations against the Bloch sphere used for manipulating the qubits of gate-based quantum computers are stated as vectors, so the calculation approach is readily used for machine learning. (Although optimization can be used for machine learning as well.) Algorithms can be grouped into these same three categories, which helps spotting areas where algorithms can be extended to accomplish additional goals. Importantly, the same quantum algorithm can underpin several different applications; for example, the algorithm that powers a financial portfolio optimization application might also underpin a separate application for route optimization. Also, the categories of applications can overlap; for instance, if you use optimization to come up with better and better answers, you may at some point come up with the exact answer, just as if you used calculation. (For instance, using optimization to find the prime factors of a large prime number, just like Shor’s algorithm, which belongs in the calculation category.) But the categories are useful for understanding the current state of quantum computing and anticipating what progress we might expect in the near future. Big potential for quantum computing There are several areas in which quantum computing could far exceed the abilities of classical computing. Following, are summaries of some of these. Cryptography Quantum cryptography is “the straw that stirs the drink” in quantum computing — a phrase first attributed to baseball great Reggie Jackson, who was working in an entirely different field (right field, to be precise). The current, fervent interest in quantum computing began in 1994 with the publication of Shor’s algorithm, which is one of the few quantum algorithms that has been proven, at this early point, to have the potential for exponential speedup. However, Shor’s algorithm will be able to do useful work only when it’s run on quantum computers far more powerful than those available today. Quantum computing has the potential to break the most common encryption methods used to secure digital communication today, such as RSA and ECC, which protect emails, bank information, the web, and more. These encryption methods rely on the difficulty of factoring large integers and the difficulty of computing discrete logarithms, respectively. Quantum computers can perform these operations exponentially faster than classical computers, making them a threat to traditional encryption methods. Quantum algorithms have been proposed for key exchange, digital signatures, and encryption, which are the building blocks of secure communication. Search algorithms Search algorithms have been an important area of research in computer science for decades. Real-world examples of the use of quantum algorithms for search include optimization problems in internet search, finance, logistics, and transportation. For example, the use of quantum algorithms for portfolio optimization will help financial analysts find the optimal investment strategy for a given portfolio in a fraction of the time required by classical algorithms. (Using quantum algorithms to optimize your portfolio works especially well if you have a quantum computer and the other investors don’t.) With the exponential growth of data, several algorithmic challenges need to be addressed. One of the biggest challenges is finding an optimal solution in a reasonable amount of time, which is where quantum algorithms come into play. One of the earliest, best-known, and most promising quantum algorithms is Grover's algorithm, used for searching an unsorted database and for a wide range of other purposes as well. For more details on these and other possible applications for quantum computing, check out our book Quantum Computing For Dummies. Financial industry applications Quantum computing is starting to make waves in the financial industry, with many companies turning to this new technology in an effort to improve their operations and gain a competitive edge. Today, quantum algorithms and applications are being explored by a variety of financial companies for uses including portfolio optimization, risk management, and fraud detection. Goldman Sachs, a leading investment bank, and several other banks are working to develop quantum algorithms for portfolio optimization; “the vampire squid,” as Goldman Sachs is sometimes called, has shown promising results in improving investment returns. By utilizing the processing power of quantum computing, this portfolio optimization effectively analyzes vast amounts of data and identifies investment opportunities that traditional algorithms might overlook, leading to more informed investment decisions. With the capability to simultaneously perform multiple calculations, quantum algorithms can help financial institutions make more informed decisions while minimizing risk and maximizing returns. Insurance risk analysis & fraud detection One area where quantum algorithms may be particularly useful in the insurance industry is in risk analysis. Insurance companies use risk analysis to determine the likelihood of a particular event occurring and the potential costs associated with that event. Quantum algorithms could greatly enhance this process by allowing for more complex calculations to be performed in a shorter amount of time. This, in turn, would allow insurance companies to better assess risk and set more accurate premiums. Another area where quantum algorithms could be beneficial in the insurance industry is in fraud detection. Fraudulent claims cost insurance companies billions of dollars each year. Detecting and preventing fraud is a top priority for many insurers. Quantum algorithms could help insurers more effectively identify fraudulent claims by analyzing large amounts of data and detecting patterns that might be difficult to spot using traditional methods. Logistics The logistics industry is constantly seeking ways to optimize its supply chain processes, and one of the latest innovations that has emerged is the use of quantum algorithms. Given the intricacies involved in supply chain optimization, quantum algorithms have the potential to be highly effective in this domain. They can facilitate the analysis of large data sets, optimize shipping routes, reduce transportation costs, and increase overall operational efficiency. One easy-to-understand example of the power of logistics is the daily route planning used by delivery company UPS. They rather famously train their drivers, and design their routes, to almost always avoid turning left. This is not some kind of political statement, but rather the result of the long waits that drivers of all vehicles sometimes suffer in getting the opportunity to safely make a left turn. By avoiding them, UPS drivers save time and money. (And might even avoid a few bent fenders along the way.) Medical science One of the most promising applications of quantum algorithms in medical science is in modeling the workings of the human body at the molecular level. Quantum computers can succeed here where classical computers fall short. One real-world example of the use of quantum algorithms is the work being done by researchers at the University of Toronto. They have used quantum algorithms to simulate the behavior of a protein involved in the development of cancer. By doing so, they were able to identify a potential drug candidate that could inhibit the protein's activity, potentially leading to new cancer treatments. Another area where quantum algorithms are showing promise is in medical imaging. MRI scans, for example, produce vast amounts of data that must be processed and analyzed to produce images of the body. Classical computers can struggle with this task, but quantum algorithms can handle it much more efficiently, which could lead to faster and more accurate diagnoses, as well as more effective treatments. Finally, quantum algorithms are used also to improve our understanding of biological systems. By simulating the behavior of complex biological systems, researchers can gain new insights into how they work and develop new treatments for diseases. Pharmaceuticals The process of developing new drugs is incredibly time-consuming and expensive, with many potential candidates failing in clinical trials. However, quantum algorithms can simulate the behavior of molecules at a level of detail that's impossible for classical computers. The effectiveness of quantum computers for this purpose means that researchers will be able to more accurately predict the effectiveness of different compounds, potentially leading to faster and more successful drug development. One of the quantum algorithms being tried for drug discovery is the variational quantum eigensolver (VQE). This algorithm is used to determine the ground state energy of molecules, which is a critical factor in drug design. The VQE algorithm uses a hybrid approach that combines classical and quantum computing to solve complex problems. It's particularly useful in drug discovery because it can accurately predict the molecular structure of compounds and their interactions with target proteins. Another quantum algorithm that has gained traction in drug discovery is the QAOA algorithm we mentioned previously. It solves optimization problems, which are common in drug discovery. The QAOA algorithm uses a series of quantum gates to optimize the energy landscape of molecules, which helps researchers identify the most promising drug candidates. Addressing climate change Climate change is a looming crisis that requires innovative solutions. The use of quantum computing and quantum algorithms could be one such solution. These technologies can help us better understand climate patterns and predict future climate changes with greater accuracy. By simulating complex systems and performing calculations at a much faster rate, quantum algorithms could help us identify ways to reduce carbon emissions, trap carbon from manufacturing processes or in ambient air, and develop more efficient renewable energy sources.

Article / Updated 09-18-2023

Quantum computing is quite different from classical computing, and there are new fundamentals and terms to learn. Two of these are the concepts of superposition and entanglement — big ideas you need to grapple with as you're learning about this new kind of computing. Superposition The state of possibility that's available to qubits is called superposition, where super means many and position means possibilities. A traditional bit can be either 0 or 1. A qubit in a state of superposition does not have a defined value because it holds many potential values at the same time. But when we measure a qubit, we just get 0 or 1 back — whichever value the qubit’s energetic wave function collapsed to when it was measured. Superposition is the first of two major pillars underpinning the power of quantum computing. The other, entanglement, is described in the next section. Welcoming foreign entanglements George Washington once warned Americans to avoid foreign entanglements. But with qubits, we welcome entanglement as an additional, powerful tool in our quantum computing toolkit. Entanglement is a kind of connection between two or more quantum particles. For instance, quantum particles have a property called spin, which we can measure as either down or up (0 or 1). If two quantum particles are entangled and one of them is measured as having an up spin, we know without measuring that the other entangled particle will have a down spin. And if we influence the spin of the first quantum particle so that it changes to up when it is measured, we know without measuring that the other quantum particle will change to down. The figure below illustrates the connection between two entangled qubits, which have opposing spins. Measuring the spin of one tells you that the spin of the other is the opposite; changing the spin of one qubit in one direction will change the spin of the other in the opposite direction. As mentioned, entanglement is the second pillar supporting the power of quantum computing. With entangled qubits, influencing a single qubit can have a knock-on effect on many others. Entanglement and superposition work together When an entangled qubit is in a state of superposition, each of its entangled connections is also in a state of superposition. These cascading uncertainties exponentially increase the potential power of quantum computers. To program and run calculations on a quantum computer, the potentiality of the entangled qubits must be maintained by keeping them coherent and free from noise. We then measure the qubits (which causes them to decohere) and record the results, a 0 or 1 for each qubit. For much more about superposition and entanglement, and all aspects of quantum computing, check out our book Quantum Computing For Dummies. Blowing past C Albert Einstein wears two hats in the history of quantum mechanics — and the two hats don’t fit comfortably on a single head. One hat comes from Einstein’s discovery of relativity, published in 1905. Relativity says that speed in this universe depends on your motion relative to other observers, but that the speed of light — about 186,000 miles per second, or 300,000 kilometers per second — is always the same for all observers. This universal speed limit is called locality. The other hat comes from Einstein’s discovery of the photon, also in 1905. (This discovery, not relativity, is the source of Einstein’s sole Nobel Prize.) The discovery of the photon is fundamental to quantum mechanics. Einstein’s problem is that quantum mechanics later asserted that quantum particles, such as photons, can be entangled with each other, so that reading the spin (for example) of one photon tells you the spin of the other. And this relationship is instantly true, without regard to the speed of light. Physicists call this an assertion of nonlocality, which is supposed to be forbidden by relativity. Einstein hated this, calling it “spooky action at a distance.” He and his colleagues spent a great deal of effort trying to disprove it, even as Einstein continued to make breakthrough quantum discoveries, such as the identification of Bose-Einstein condensates, which are superconducting gases that can be used to create qubits. Today’s mainstream computers are subject to classical mechanics and limited by the speed of light. Quantum computers depend on quantum mechanics and, in their use of entanglement, are not limited by light speed. The Nobel Prize for Physics in 2022 was awarded to physicists who showed that entanglement is real. So researchers in quantum computing who depend on entanglement can say, after Galileo: “And yet it computes.” (Galileo, on trial for asserting — correctly, as it turned out — that Earth is not at the center of the universe, is famously said to have whispered: “And yet it moves.”) Enabling quantum computing with coherence Qubits can be used for quantum computing only when they’re kept in a state of coherence, free of interaction with their environment. To do quantum computing, qubits need to follow the rules of quantum mechanics, and these rules apply to only coherent qubits. Quantum particles zipping around the universe — photons emitted by the sun, for example — are in a state of coherence. What causes them to decohere? Any interaction with excessive interference (such as vibration or a strong magnetic field), a solid object, or a measuring device. Keeping qubits coherent is hard. Heat decoheres them, so qubits are kept cold. So do vibration (think of a truck going by on a road) and any collision with their environment. To prevent such collisions, qubits often use strong magnetic fields or targeted laser beams to prevent the quantum particles inside them from colliding with their physical containers. Decoherence is not the only disaster that can affect qubits. Temperature changes, vibration, or physical interaction may change the value of a qubit in an uncontrolled manner without causing it to decohere. This noise causes errors in the results of quantum computations. Minimizing noise and detecting errors are two of the biggest challenges facing quantum computers. To manipulate each qubit — to program it, for instance, for quantum computing — the qubit must be controlled in such a way as to adjust its value without causing it to decohere. Magnetic fields and laser beams are among the means used to manipulate qubits without causing decoherence. When we measure the value of a qubit, two things happen: The qubit decoheres, becoming subject to the rules of classical mechanics. The qubit’s value collapses from somewhere between 0 and 1, inclusive, to either 0 or 1. The qubit must be reinitialized — returned to coherence — before it can be used again for computing. Some argue that the potential of quantum computers is very limited — that the level of coherence needed for quantum computers to achieve useful results is impossible, in theory and in fact. In the extreme version of this argument, leaders in quantum computing are accused of deliberately committing fraud, which would mean that the entire field is a massive conspiracy. Only further work will show the limits to quantum computing, if any, but the fraud allegations are just a conspiracy theory. The math for the power of quantum computing It’s challenging to fully grasp the potential power of quantum computing compared to classical computing because that power is based on quantum mechanical principles. But we can sum it up in just a bit of math. Because the bits in classical computing can hold only one of two values — a 0 or a 1 — at the same time, the number of states that a classical computer can hold is represented by the number of bits, n, to the power of two: n2. But a set of entangled qubits can hold all the possible values of the qubits at the same time. For this reason, the number of states that a quantum computer can hold is represented by two to the power of qubits, n: 2n. For example, to represent a million possible states would require 1,000 bits but only 20 qubits. Today’s computers contain billions of bits, but we have to throw a lot of them at our most complex problems to get anywhere. Today’s quantum computers have a small number of qubits — a recent IBM quantum computer release clocked in with 433 — but we need only a few hundred qubits to begin tackling very complex problems. The power of today’s quantum computers is limited by errors and short coherence times. But as these factors are addressed, the results are likely to be amazing. What will quantum computing do for people? It’s easy to spend time geeking out on the strangeness and power of quantum computing. But what difference will quantum computing make to humanity? To understand the answer, we first have to address a common misconception. People today tend to worry about how powerful today’s computers are: to worry about the power of the internet, social media, and machine learning and AI. But there’s also a big problem around how powerful today’s computers aren’t: They simply aren’t up to big computational challenges in areas such as better batteries to fight climate change, better aerodynamics, better routing in complex transportation networks, and better discovery of new drugs, to name a few important examples. And these big computational challenges are exactly the areas where we expect quantum computing to make a big difference. Future quantum computers will be able to solve problems we can’t touch today, and to do so far faster, more cheaply, and with less energy expenditure than today’s computers. Quantum computers can only “do their thing” in partnership with computers of the kind we use today. So, when you see descriptions of what quantum computing can do, understand that these accomplishments will also require a whole lot of conventional computing power.

Cheat Sheet / Updated 09-05-2023

Have you heard about quantum computing? Do you want to learn more? Is programming a quantum computer in your future? Read on to learn some key terms, to discover the different kinds of quantum computing approaches, to survey the wonderful world of qubits, and to learn how to get yourself some class. (One or more online classes, that is.)

Article / Updated 08-10-2023

You can transfer files yourself if you're moving from a Windows 7, 8, 8.1, or 10 PC. You can do this with a combination of a Microsoft account and the built‐in File History backup program in Windows. You tell the program to back up your old PC's files, and then you tell your new PC's program to restore the files. However, you need a portable hard drive for this to work. Portable hard drives are fairly inexpensive, usually costing less than $100. But there's a bonus: When you're through transferring the files, the drive works perfectly for backing up your new computer. To transfer files from an old Windows 7, 8, 8.1, or 10 computer to a new Windows 10 computer, follow these steps: If you're running Windows 7 on your old PC, upgrade it to Windows 10.For many Windows 7 owners, this is probably a deal breaker. Unless, of course, you took advantage of the free Windows 10 upgrade offer that ended July 29, 2016. Now that the deadline has passed, Windows 7 owners might be better off by buying a file transfer program.If you're running Windows 8, 8.1, or 10 on your old PC, move ahead to Step 2. If you've already been using File History on your old PC, jump to Step 5. Otherwise move to Step 3. Sign in with your Microsoft account on your old PC.When you sign in with a Microsoft account, Microsoft remembers many of your settings and services so it can duplicate them on other PCs you sign into. Plug the portable hard drive into your old PC and then set up File History to save your files onto the portable hard drive.File History comes built into Windows 8, 8.1, and 10. It could take anywhere from a few minutes to a few hours to back up your files for the first time.While File History backs up your files, it shows the statement "File History is saving copies of your files for the first time." (It also lists the word Stop in case you want to stop the backup.) When File History has finished backing up your files to the portable drive, those words change to say "Files last copied," followed by the date and time it finished backing up your files, as shown. At that point, move to Step 5. Sign into your new Windows 10 PC with the same Microsoft account you used on your old PC. Then plug the portable hard drive into your new computer.By signing in with your Microsoft account, your settings automatically transfer to your new PC. (The wallpaper on your new PC quickly changes to match your old PC, letting you know that something is happening.) Open File History and direct your new Windows 10 PC toward your old File History backup. On your new Windows 10 PC, click the Start button and type File History into the Search box and press Enter. The Control Panel's File History window appears, as shown. Click the check box labeled I Want to Use a Previous Backup on this File History Drive. A window drops down, listing the backup you've made on your old PC. Click its name, and click the Turn On button. Your new PC begins backing up its files for the first time, but these incoming files won't damage your old PC's backup. Choose Restore Personal Files from the File History window's left pane. Choose the files and folders to restore and then click the green Restore button. Click the Forward or Back arrows next to the big green button along the window's bottom until you find the date and time of the files you'd like to restore.For example, if you used File History on your old PC for the first time in Step 4, click the Back arrow (on the left) until you're at the Number 1 backup. If you've been using File History on your old PC all along, click the Forward arrow (on the right) to move to your most recent backup. When you're viewing the files or folders you want to restore, click the green button found on the window's bottom edge, shown here. File History begins copying your old PC's files and folders onto your new PC. If there are no complications, your new PC should soon have the files and folders from your old PC. If you'd already been using File History on your old PC, all of your old PC's backups should still be available to you on your new PC. Your new PC will continue to back up your new computer's files to your portable hard drive. Keep the hard drive plugged in permanently. (Or, if you bought a new laptop or tablet, plug it in frequently so your computer can keep your backups current.) If you've just borrowed a friend's portable hard drive, you can unplug it at this point and give it back. But you should really have your own portable hard drive so you can begin backing up your new Windows 10 PC. Your Microsoft account and File History can transport your settings and files to your new PC. However, you must still install all of your old desktop programs onto your new PC. If you're moving to Windows 10 from a Windows 8 or 8.1 PC, you can find your apps waiting for you in the Windows Store: Click your icon near the Store app's upper‐right corner and choose My Library from the drop‐down menu. There you can find and download your old apps to your new PC.

Article / Updated 07-10-2023

You want to get your hands on your credit report so you know what lenders are reviewing. You're entitled to receive a free copy of your credit report (which does not contain your credit score) every 12 months from each of the three credit bureaus — Equifax, Experian, and TransUnion. If you visit this website, you can view and print copies of your credit report from each of the three credit agencies. (Alternatively, you can call 877-322-8228 and request that your reports be mailed to you.) When you receive your reports, inspect them for possible mistakes. Credit-reporting bureaus and the creditors who report credit information to these bureaus make plenty of errors. If your problems are fixable, there's no need to hire someone to do so for you — you can direct getting them fixed yourself, but you will likely have to make some phone calls or write a letter or two. Some credit-report errors arise from other people's negative information getting on your credit report. This can happen if you have a common name, have moved a lot, or for other reasons. If the problematic information on your report appears not to be yours, tell that particular credit bureau and explain that you need more information because you don't recognize the creditor. Creditors are the source of some reporting mistakes as well. For example, perhaps a bill you paid off is still incorrectly being reported as a balance you owe. If that's the case with your report, write or call the creditor to get the incorrect information fixed. Phoning first usually works best. (The credit bureau should be able to tell you how to reach the creditor if you don't know how.) If necessary, follow up with a letter or an email. You can also dispute errors online directly with the credit reporting agency. Whether you speak with a credit bureau or an actual lender, make notes of your conversations. If representatives say that they can fix the problem, get their name and extension, and follow up with them if they don't deliver the promised results. If you're ensnared in bureaucratic red tape, escalate the situation by speaking with a department manager. By law, bureaus are required to respond to a request to fix a credit error within 30 days. And if you file a dispute and the creditor doesn't respond, the credit bureau must then remove the derogatory item. You and a creditor may not see eye to eye on a problem, and the creditor may refuse to budge. If that's the case, credit bureaus are required by law to allow you to add a 100-word explanation to your credit file. Just remember that if you go this route, be factual in your write-up and steer clear of broad attacks on the creditor (such as "their customer service sucks"). Avoid "credit-repair" firms that claim to be able to fix your credit report problems. In the worst cases I've seen, these firms charge outrageous amounts of money and don't come close to fulfilling their marketing hype. If you have legitimate glitches on your credit report, credit-repair firms can't make the glitches disappear. You can easily fix errors on your own without the charge.

Article / Updated 07-10-2023

When most people hear the word budgeting, they think unpleasant thoughts, like those associated with dieting, and rightfully so. Who wants to count calories or dollars and pennies? But budgeting — planning your future spending — can help you move from knowing how much you spend on various things to reducing your spending. The following process breaks down budgeting in simple steps: Analyze how and where you're currently spending. Calculate how much more you want to save each month. Determine where to make cuts in your spending. Suppose you're currently not saving any of your monthly income and you want to save 10 percent for retirement. If you can save and invest through a tax-sheltered retirement account — such as a 401(k), 403(b), SEP-IRA, and so forth — then you don't actually need to cut your spending by 10 percent to reach a savings goal of 10 percent of your gross income. When you contribute money to a tax-deductible retirement account, you generally reduce your federal and state income taxes. If you're a moderate-income earner paying approximately 30 percent in federal and state taxes on your marginal income, you actually need to reduce your spending by only 7 percent to save 10 percent. The other 3 percent of the savings comes from the lowering of your taxes. (The higher your tax bracket, the less you need to cut your spending to reach a particular savings goal.) So to boost your savings rate to 10 percent, you simply need to go through your current spending, category by category, until you come up with enough proposed cuts to reduce your spending by 7 percent. Make your cuts in areas that are the least painful and in areas where you're getting the least value from your current level of spending. If you don't have access to a tax-deductible retirement account or you're saving for other goals in nonretirement accounts, budgeting still involves the same process of assessment and making cuts in various spending categories.

Article / Updated 07-05-2023

People typically learn their financial habits, both good and not so good, at a young age. During childhood, most people are exposed to messages and lessons about money, both at home with their parents and siblings and also in the world at large, such as at school and with their friends. The expression "You can't teach an old dog new tricks" has some validity, at least for our four-legged friends, but even then, the expression actually requires some modification to be accurate. It should be, "It's hard to teach an old dog new tricks, but how hard it is depends on the dog." The same is true for people and their financial habits and decision making. For most people, spending money is easier and more enjoyable than earning and saving it. Of course, you can and should spend money, but there's a world of difference between spending money carelessly and spending money wisely. Here are some tips and tricks so you can get even better at saving more and spending less: Live within your means. Spending too much is a relative problem. If you spend $40,000 per year and your income is $50,000 annually, you should be in good shape and will be able to save a decent chunk of your income. But if your income is only $35,000 per year and you spend $40,000 annually, you'll be accumulating debt or spending from your investments to finance your lifestyle. How much you can safely spend while working toward your financial goals depends on what your goals are and where you are financially. At a minimum, you should be saving at least 5 percent of your gross annual (pretax — that is, before taxes are deducted from your paycheck) income, and ideally, you should save at least 10 percent. Search for the best values. The expression "You get what you pay for" is an excuse for being a lazy shopper. The truth is that you can find high quality and low cost in the same product. Conversely, paying a high price is no guarantee that you're getting high quality. When you evaluate the cost of a product or service, think in terms of total, long-term costs. Buying a cheaper product only to spend a lot of additional money servicing and repairing it is no bargain. Research options and comparison shop to understand what's important to you. Don't waste money on bells and whistles that you don't need and may not ever use. Is that $700 smartphone significantly better than the best $200 smartphones? Don't assume brand names are the best. Be suspicious of companies that spend gobs on image-oriented advertising. Branding is often used to charge premium prices. Blind taste tests have demonstrated that consumers can't readily discern quality differences between high- and low-cost brands with many products. Question the importance of the name and image of the products you buy. Companies spend a lot of money creating and cultivating an image, which has no impact on how their products taste or perform. When you're grocery shopping, consider the store or house brand. Most of the time the ingredients are the same as the brand-name product (and may even be made by that same company). You don't need to shell out money to pay for the name, as store/house brands are typically much less costly than the well-known brands in a given category. Get your refunds. Have you ever bought a product or service and not gotten' what was promised? What did you do about it? Most people do nothing and let the company off the hook. Ask for your money back or at least a partial refund. If you don't get satisfaction from a frontline employee, request to speak with a supervisor. Most larger companies have websites through which you can submit complaints. Reputable companies that stand behind their products and services will offer partial refunds or gift cards good toward a future purchase. If all else fails and you bought the item with your credit or debit card, dispute the charge with the credit-card company. You generally have up to 60 days to dispute and get your money back. Trim your spending fat. What you spend your money on is sometimes a matter of habit rather than a matter of what you really want or value. When was the last time you comparison priced and shopped for the most common things that you buy? You need to set priorities and make choices about where you want and don't want to spend your money. Turn your back on consumer credit (for example, credit-card debt, auto loans). Borrowing money to buy consumer items that depreciate (such as cars and electronics) is hazardous to your long-term financial health. Buy only what you can afford today. If you'll be forced to carry a debt on credit cards or an auto loan for months or years on end, you can't really afford what you're buying on credit today. Not only does consumer debt enable you to spend more than you can afford today, but the interest rate on that consumer debt is generally high, and it isn't tax-deductible. If you spend too much and spend unwisely, you put pressure on your income and your future need to continue working, perhaps at a job that you don't really enjoy. Savings dwindle, debts may accumulate, and you won't be able to achieve your personal and financial goals. Living within your means and continually growing your savings can give you more freedom, choices, and comfort with taking some risks (for example, changing careers, leaving your job to raise children, joining a start-up or starting your own company, and so on) that you may not otherwise feel as comfortable taking.

Cheat Sheet / Updated 05-08-2023

Whether you’ve purchased a new Mac with macOS Ventura pre-installed or you’ve upgraded from a previous version of macOS, you’ll find that Ventura makes your computer easier to use and offers myriad improvements to make you more productive. This Cheat Sheet includes information on things you should never do to your Mac; a compendium of useful and timesaving keyboard shortcuts; recommendations for backing up data; and website recommendations for smart Ventura users.